Reptile carpet won't work for large beardies, snagging nails and then a nightmare to keep clean after a large poo. Better off with non adhesive shelf liner, nothing too slippery, or plain old newspaper. I don't like ceramic tile either. esp. if a dragon has a hurt leg. I used to use a topsoil/sand mix in one of my largest enclosures, beardies love it. BTW, is his leg swollen ?
Your choice of lighting is extremely important, what type of uvb do you have ? Look carefully for the brand, nae + wattage. Is it a long tube, is it on top of the screen ? Post a pic of all the lighting, showing the actual bulbs. Without good uvb, beardies can't absorb calcium, even if they are given it daily.
Can you take him outside in the sun for natural uvb daily ? Not in a glass tank, but just sitting in the grass with him. That may help strengthen his bones.